Does the instruction in Transition
Mathematics provide an opportunity for students to learn the benchmark ideas and
skills?Numerous sightings were analyzed to determine the instructional
criteria ratings for TYPICAL SIGHTING CHART (Adobe PDF document) The graph below depicts major strengths and weaknesses in the overall instructional
guidance provided by Transition Mathematics received on each of the 24 instructional
criteria, across all six of the benchmarks used for the evaluation.INSTRUCTION HIGHLIGHTS CHART (Adobe PDF document)
Overall, analysts rated
Although most of the activities are consistent with the purpose of the chapter, it is not clear that they would be interesting or motivating to students. Teachers are provided with notes about the introductions but are given no direction regarding discussions or opening activities that relate to the purpose. The text provides end-of-section questions for self-progress checks that relate to the overall purpose of the unit. Each section has the same components: introductory comments with a picture, diagram, graph, or chart; examples that lead to the development of specific problem-solving algorithms; and practice problems that address the specific skills/strategies just developed. There is no stated rationale for the sequence of activities.
There are numerous activities that directly address the ideas in the benchmarks; however, only a few of them deviate from pencil and paper or calculator activities. There are many opportunities for students to apply the skills in the benchmarks through problem solving, but few questions address when and why students should do procedures. There are a variety of skill development activities, but few of them would be meaningful or interesting to most students.
While each section has some kind of introductory paragraph, these are brief and often fail to develop a comprehensible argument for why the mathematics makes sense. New terms are introduced in bold face at the beginning of sections with formal definitions and principles that students use immediately. Representations of concepts are shown through examples that would likely be comprehensible to students. Connecting concepts are presented at the beginning of each section where students are shown a strategy for applying the concepts and then given the opportunity to practice with applications. There are a sufficient number of practice exercises, although few of them are novel or use interesting situations.
Instructional Category V
The examples that ask the students to explain how to do a procedure fail to require
students to explain their thinking or reasoning about why the procedure works.
Instructional Category VI
Assessment items for both the skills and concepts benchmarks are available; however, fewer items address the substance of the conceptual benchmarks. Even though the material includes several types of assessment items, the applications are mainly routine calculations done with pencil and paper. Embedded assessments are present, but they do not go beyond the students’ initial responses, and there are no suggestions to teachers for modifying or adapting learning activities based on how students perform.
Instructional Category VII
Content information provided for teacher learning is effective for the number
benchmarks but not for the geometry and algebra benchmarks. |